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Full text of "Text Book Of Mechanical Engineering"

Appendix II

847'

(b)

-,and 2nd moment = 2 {PPI x e x (PN)2}
(<? x // x PQX x PN) ...        ...    by substitution from (a)

(<? x #* x PQ2)         ......    by substitution from ()

= ffi x 2 0 x PQ2) = A2/fr2

r moments may be similarly proved.

the construction to beam sections, we must first find
Imagine any given section ab (Fig. Bio).    Find its

-----^1   LINE    OF             \CU       LIMITING STRESS   j.

X,

o-f

^b                          X

loment Ax, round xx say, using any height //. Dealing only
he right-hand half for simplicity, we have from the definition
itre-of-gravity,

A^ = A G                   Hence, G =  

gives the height of neutral axis z z by a much more simple
ccurate method than those on p. 432, especially if a plani-

is obtainable. We next require I, the 2nd moment, round
ting preferably the reference distance y to line of limiting

in constructing the curves. Treating the left side, to avoid
ion, every horizontal strip is referred to //, and its projection

to ^producing if necessary, till the original strip is crossed ;
hus the areas a a\ are found, on opposite sides of the
L] centre line. Continuing the process on areas a a\, the